even the dictionaries don't agree.
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RANDOM HOUSE WEBSTER'S DICTIONARY:
MUSICIAN: a person who performs OR composes music


MUSIC: the art of ordering sounds into cohesive and structured forms


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FUNK & WAGNALL'S standard desk dictionary:

MUSICIAN:
1) A professional performer or composer of music
2) one skilled in performing or composing music

MUSIC:
1) a succession or combination of musical sounds, especially if the sounds are pleasing to the ear

2) the art of producing significant arrangements of sounds, usually with reference to rhythm, pitch and tone

3) a musical score

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DICTIONARY.COM

MUSICIAN:
1) a person who makes music a profession, especially as a performer of music.

2) any person, whether professional or not, skilled in music.


MUSIC:
1) an art of sound in time that expresses ideas and emotions in significant forms through the elements of rhythm, melody, harmony, and color.

2) the tones or sounds employed, occurring in single line (melody) or multiple lines (harmony), and sounded or to be sounded by one or more voices or instruments, or both.

3) musical work or compositions for singing or playing.

4) the written or printed score of a musical composition.